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All Journal Paradikma: Jurnal Pendidikan Matematika JPMI (Jurnal Pendidikan Matematika Indonesia) JURNAL PENDIDIKAN MIPA MES: Journal of Mathematics Education and Science JURNAL PEMBELAJARAN DAN MATEMATIKA SIGMA (JPMS) Jurnal Educatio FKIP UNMA Mandalika Mathematics and Educations Journal Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika Griya Journal of Mathematics Education and Application JagoMIPA: Jurnal Pendidikan Matematika dan IPA SCIENCE : Jurnal Inovasi Pendidikan Matematika dan IPA Dharmas Education Journal (DE_Journal) Kognitif: Jurnal Riset HOTS Pendidikan Matematika Humantech : Jurnal Ilmiah Multidisiplin Indonesia Jurnal Didactical Mathematics Jurnal Pengabdian Masyarakat dan Riset Pendidikan EduInovasi: Journal of Basic Educational Studies Jurnal Pendidikan dan Sosial Humaniora
Michael Christian Simanullang
Universitas Negeri Medan
Religion Humanities Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Library & Information Science Mathematics Physics Public Health Social Sciences Other

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PENGARUH AUGMENTED REALITY TERHADAP PEMAHAMAN KONSEP BARISAN PADA MAHASISWA Lubis, Ariyanto; Purba, Diva Novita Angely Putri; Simangunsong, Erika; Simanullang, Michael Christian
Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika Vol. 6 No. 1 (2025): Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistik
Publisher : LPPM Universitas Bina Bangsa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46306/lb.v6i1.925

Abstract

Technological advances in education have brought significant changes in learning methods, including the use of Augmented Reality (AR) as an interactive media to improve students' understanding of the concept of rows. This study aims to analyze the effect of using AR on the understanding of the concept of sequence in the Real Analysis course, especially in the aspects of sequence limit, sequence tail, and sequence operation. The approach used in this research is qualitative with descriptive analysis method, where the data is collected through tests given to three students who are the research subjects. Augmented reality developed in this study visualizes the concept of limit of a line by displaying points that are getting closer to the x-axis, as well as adding elements of the tail of the line to test students' understanding of the part of a line. The results showed variations in students' level of understanding of each concept tested, and revealed some conceptual errors that occurred during the testing process. The discussion in this study highlights the effectiveness of AR in facilitating student understanding, as well as identifying factors that influence success in understanding the concept of rows in more depth.
STUDI KESULITAN MAHASISWA DALAM MEMPELAJARI DERET TAK HINGGA : STUDI KASUS DI JURUSAN MATEMATIKA UNIMED Rahmadani, Nisa; Aulia, Cut Najwa; Laia, Lukman Hakim; Maigani, Maigani; Simanullang, Michael Christian
Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika Vol. 6 No. 1 (2025): Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistik
Publisher : LPPM Universitas Bina Bangsa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46306/lb.v6i1.930

Abstract

infinite series is an important concept in mathematics which often becomes a challenge for students. This study aims to analyze the difficulties faced by students of the Mathematics Department at Medan State University (UNIMED) in understanding and solving problems related to infinite series. This research uses a survey method with a questionnaire given to students who have studied this material. The research results show that the students' main difficulties lie in understanding the concept of convergence, using the convergence test, and applying it in problem solving. Based on the research results, it is recommended that there is a more interactive and technology-based learning approach to increase student understanding
Analisis Pemahaman Mahasiswa Terhadap Konsep Bilangan Real Dalam Analisis Matematika Sinurat, Ade Putra; Barus, Harry Aprianto; Simanullang, Michael
Jurnal Educatio FKIP UNMA Vol. 11 No. 3 (2025)
Publisher : Universitas Majalengka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31949/educatio.v11i3.13376

Abstract

Bilangan real merupakan fondasi fundamental dalam matematika, namun mahasiswa sering menghadapi kesulitan dalam memahami konsep-konsep dasarnya. Penelitian sebelumnya menunjukkan adanya kesenjangan dalam pemahaman integratif terhadap struktur bilangan real. Tujuan: Penelitian ini bertujuan menganalisis konsep-konsep fundamental bilangan real dan mengidentifikasi keterkaitan sistemik antar konsep untuk memberikan kerangka teoritis yang komprehensif. Penelitian menggunakan desain kualitatif dengan pendekatan studi kepustakaan deskriptif-analitis. Sampel terdiri dari 25 sumber literatur yang dipilih secara purposive (15 artikel jurnal, 8 buku referensi, 2 laporan penelitian) periode 2014-2025. Data dianalisis menggunakan teknik analisis isi dengan pendekatan deduktif-induktif melalui matriks analisis literatur. Penelitian mengidentifikasi tujuh konsep kunci: elemen maksimum-minimum, prinsip induksi matematis, prinsip terurut dengan baik, sifat aljabar dan urutan pada ℝ, ketaksamaan Bernoulli, nilai mutlak, dan persekitaran. Temuan menunjukkan bahwa 87% sumber menekankan pentingnya elemen maksimum-minimum dalam kelengkapan bilangan real, 92% sumber mengkonfirmasi ekuivalensi prinsip induksi dengan prinsip terurut, dan semua konsep membentuk hierarki yang saling terkait. Konsep-konsep fundamental bilangan real membentuk struktur teoritis yang koheren dan self-consistent. Penelitian memberikan kerangka integratif untuk pembelajaran bilangan real dan basis teoritis untuk pengembangan strategi pedagogis yang lebih efektif dalam pendidikan matematika tingkat lanjut.
Analisis Analisis Kesalahan Mahasiswa dalam Menjawab Soal Barisan Cauchy berdasarkan Teori Newman Sarah, Siti; Sulaiman, Raysah Puteri; Hutapea, Yonata; Tarigan, Septi Agita; Simanullang, Michael Christian
Mandalika Mathematics and Educations Journal Vol 7 No 2 (2025): Edisi Juni
Publisher : FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jm.v7i2.8960

Abstract

This study aims to identify the types of reading errors made by students in solving Cauchy sequence problems in a Real Analysis course. The research employed a descriptive qualitative method using Newman's theory as the analytical framework. The subjects were Mathematics Education students at Universitas Negeri Medan who had completed the course. The results revealed that students made errors in reading, understanding the problems, and performing calculation procedures, particularly in grasping the fundamental concept of Cauchy sequences. These findings highlight the need to strengthen conceptual understanding through more targeted learning strategies and the application of Newman’s theory as a tool for diagnosing errors.
A Analisis Kessalahan Mahasiswa Dalam Menyelesaikan Soal Barisan Monoton Dengan Perspektif Teori Kastolan Nainggolan, Gustia Louisa; Siregar, Dea Athalia; Dhuha, Nadira Kaylana; Sinurat, Putra Paulus; Simanullang , Michael Christian
Mandalika Mathematics and Educations Journal Vol 7 No 2 (2025): Edisi Juni
Publisher : FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jm.v7i2.8963

Abstract

This study aims to analyze the types of errors made by students in solving problems involving Monotonic Sequences, using Kastolan’s error theory as the analytical framework. A qualitative descriptive approach was adopted, involving three students from a Mathematics Education Study Program as research participants. Data were collected through problem-solving tasks distributed via Google Forms and analyzed based on Kastolan’s error categories. The data analysis process consisted of three stages: data reduction, data presentation, and conclusion drawing. The findings revealed that procedural errors were the most dominant, occurring in 66% of the responses and classified as very high. Conceptual errors followed with a percentage of 33%, categorized as moderately high. Technical errors appeared least frequently, with a percentage of 11%, and were categorized as low. These results indicate that students face difficulties in following systematic steps during problem-solving. Therefore, educators are encouraged to reinforce students’ procedural skills by implementing learning strategies that are more structured, focused, and effective.
Analisis Kesalahan Mahasiswa Pendidikan Matematika Dalam Menyelesaikan Soal Deret Tak Hingga Berdasarkan Teori Kastolan Sitorus, Grace Elicia; Sibarani, Khoirunnisa; Samosir, Martha Indah; Manurung, Hendra Cahyadi; Simanullang, Michael Christian
Mandalika Mathematics and Educations Journal Vol 7 No 2 (2025): Edisi Juni
Publisher : FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jm.v7i2.8970

Abstract

This study analyzes errors made by mathematics education students in solving problems related to infinite series, focusing on a topic known for its conceptual and procedural complexity. Based on Kastolan's Theory, this research builds upon previous findings regarding students’ difficulties with infinite series material. A qualitative descriptive approach was employed to analyze the responses of 10 mathematics education students at Universitas Negeri Medan, who had taken or were currently taking the real analysis course, particularly the topic of infinite series. The participants were randomly selected. Data were collected through a structured Google Form questionnaire and two open-ended questions assessing convergence and the summation of geometric series. The errors were categorized into three types: conceptual errors, such as misinterpretation of convergence criteria (10%); procedural errors, including incorrect determination of the ratio (30%); and technical errors, such as calculation mistakes (40%), with percentages calculated using the formula . The findings indicate that while conceptual understanding was relatively sound, technical errors were most prevalent, especially in fraction operations and symbolic manipulation. The study recommends instructional approaches that integrate concept reinforcement, procedural scaffolding, and computational accuracy training. This research contributes to mathematics education by providing empirical evidence on common error patterns in advanced calculus and by encouraging instructors to strengthen teaching strategies that systematically combine conceptual understanding and procedural skills in solving infinite series problems.
Identifikasi Kesalahan Mahasiswa dalam Menyelesaikan Soal Induksi Matematika pada Analisis Real: Perspektif Teori Kastolan Fadilla, Nia; Andini, Putri; Masita, Nurul; Waniza, Elva; Sinaga, Sinta Marintan; Simanullang, Michael Christian
Mandalika Mathematics and Educations Journal Vol 7 No 2 (2025): Edisi Juni
Publisher : FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jm.v7i2.8978

Abstract

This study aims to identify and analyze the types of errors made by students in solving Mathematical Induction problems using Kastolan's theory. The analysis results are expected to clarify the specific difficulties faced by students and serve as a basis for improving the quality of mathematics education at the higher education level. This research employs a descriptive qualitative approach with ten sixth-semester students from the Mathematics Education Study Program at Universitas Negeri Medan as subjects. Data were collected through written tests, interviews, and documentation, and analyzed using the Miles and Huberman model, which includes data reduction, data display, and conclusion drawing. The results show that students made three main types of errors: procedural errors (50%), technical errors (27.27%), and conceptual errors (22.72%). Procedural errors were the most dominant, indicating a lack of understanding of the systematic steps required in inductive proofs. The primary cause of these errors was the students' insufficient comprehension of mathematical induction material during lectures. Therefore, a learning approach that emphasizes understanding logical structures and proof procedures is necessary to enhance the quality of mathematics instruction in higher education.
Analisis Kesalahan Mahasiswa Dalam Menyelesaikan Soal Limit Fungsi Berdasarkan Teori Kastolan Tanjung, July Yanty; Simanjuntak, Rosi Ade Putri; Manullang, Juliana Citra; Turnip, Leonardo; Simanullang, Michael Christian
Mandalika Mathematics and Educations Journal Vol 7 No 2 (2025): Edisi Juni
Publisher : FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jm.v7i2.9014

Abstract

This study aims to identify the causes of errors made by students in solving limit function problems. Limit concepts often present challenges to students due to their complexity, which can lead to confusion. In this research, four students from the Mathematics Education Program at Universitas Negeri Medan served as the subjects, participating in interviews and written tests. They were given limit problems to assess their difficulties in understanding the material. The findings revealed a variety of errors made by the students. Approximately 75% of these errors were due to their inability to organize proper solution steps and incorrect application of formulas. Additionally, 50% of the errors resulted from a lack of understanding of the definition of limits, while 25% were attributed to calculation mistakes or oversights. These results indicate that many students still struggle with the fundamental concepts of limits and the correct methods for solving these problems. To improve student comprehension in this area, it is recommended to implement more interactive and focused teaching methods, enabling them to better grasp the concepts of limits and the appropriate techniques for problem-solving.
Analisis Pemahaman Mahasiswa Terhadap Konsep Interval Dalam Mata Kuliah Analisis Real Christian Simanullang, Michael; Berutu, Jhosua; Indri Agista Lubis, Nazwah; Yolanda Marylandia Sitorus, Tabhita; Maria Munthe, Tiolina
Mandalika Mathematics and Educations Journal Vol 7 No 2 (2025): Edisi Juni
Publisher : FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jm.v7i2.9071

Abstract

This study aims to analyze students' understanding of the concept of interval in the Real Analysis course, particularly in understanding the properties of intervals, such as supremum, infimum, and nested intervals. The research method used is a qualitative descriptive approach with a case study. Data were collected through proof-based essay tests, semi-structured interviews, and participant observation during the learning process using GeoGebra 3D AR. The sample consisted of 35 fourth semester students from the Mathematics Education program enrolled in the Real Analysis course. Data analysis was carried out with a thematic approach based on the APOS theory (Action, Process, Object, Schema). The results showed that most students struggled to transfer the visual understanding obtained through GeoGebra 3D AR into formal proofs. While 68.6% of students showed an improvement in visual understanding, only 8.5% could formally prove the property of nested interval intersections. The implications of this study highlight the importance of integrating interactive technology with deeper proof exercises, as well as the application of problem-based approaches to enhance understanding of the interval concept. The limitations of this study include the small sample size and the focus on one type of learning technology. Future research is recommended to explore the use of other technologies and more varied teaching methods.
ANALISIS MISKONSEPSI MAHASISWA DALAM MENYELESAIKAN SOAL SUPREMUM DAN INFIMUM BERDASARKAN TEORI NEWMAN Sihotang, Harry Marcel Wahyu; Sitindaon, David Micle; Saing, Nasib Maruli Tua; Silalahi, Lisbeth Grace Luciana; Sinaga, Debora; Simanullang, Michael Christian
SCIENCE : Jurnal Inovasi Pendidikan Matematika dan IPA Vol. 5 No. 2 (2025)
Publisher : Pusat Pengembangan Pendidikan dan Penelitian Indonesia (P4I)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.51878/science.v5i2.5090

Abstract

This study aims to analyze students' misconceptions in solving problems related to the concepts of supremum and infimum in Real Analysis courses. These concepts are fundamental in mathematics, yet many students struggle to understand and apply them correctly. Using a qualitative approach and Newman’s Error Analysis theory, this research identifies the stages of errors made by 8 Mathematics Education students at Universitas Negeri Medan through a written test consisting of three problems. Data were descriptively analyzed based on Newman’s five error stages: reading error, comprehension error, transformation error, process skill error, and encoding error. The results reveal that the most dominant errors occur at the comprehension stage, where students frequently confuse supremum/infimum with maximum/minimum values. Transformation and process skill errors were also significant, particularly in problem modeling and computational operations, while encoding errors reflected inaccuracies in presenting final answers. These findings highlight the need for teaching strategies that emphasize conceptual understanding, in-depth discussions, and visualization tools. Adaptive scaffolding and intensive practice are recommended to address student misconceptions. This study contributes to the development of more effective Real Analysis teaching methods and opens opportunities for further error-diagnosis-based research. ABSTRAKPenelitian ini bertujuan untuk menganalisis miskonsepsi mahasiswa dalam menyelesaikan soal-soal terkait konsep supremum dan infimum pada mata kuliah Analisis Real. Konsep ini merupakan fondasi penting dalam matematika, namun banyak mahasiswa mengalami kesulitan dalam memahami dan menerapkannya secara tepat. Studi kualitatif ini menggunakan teori Analisis Kesalahan Newman untuk mengidentifikasi tahapan kesalahan yang dilakukan oleh 8 mahasiswa Program Studi Pendidikan Matematika Universitas Negeri Medan melalui tes tertulis yang mencakup tiga soal. Data dianalisis secara deskriptif berdasarkan lima tahapan kesalahan Newman, yaitu reading error, comprehension error, transformation error, process skill error, dan encoding error. Hasil penelitian menunjukkan bahwa kesalahan paling dominan terjadi pada tahap pemahaman (comprehension error), di mana mahasiswa sering keliru membedakan supremum/infimum dengan nilai maksimum/minimum. Kesalahan transformasi (transformation error) dan proses penyelesaian (process skill error) juga signifikan, terutama dalam memodelkan soal dan melakukan operasi perhitungan, sementara kesalahan pengkodean (encoding error) mencerminkan ketidaktepatan dalam menyajikan jawaban akhir. Temuan ini mengindikasikan perlunya pendekatan pembelajaran yang menekankan pemahaman konseptual, diskusi mendalam, dan penggunaan alat visualisasi. Strategi seperti scaffolding adaptif dan latihan intensif direkomendasikan untuk memperbaiki miskonsepsi mahasiswa. Penelitian ini memberikan kontribusi bagi pengembangan metode pembelajaran Analisis Real yang lebih efektif serta membuka peluang penelitian lanjutan berbasis diagnosis kesalahan.
Co-Authors Ambarita, Zefanya Tabita Ananda, Rizky Angel Ramayanti Samosir Angraini, Shepia Arsandy, Qory Septiani Aulia, Cut Najwa Barus, Harry Aprianto Berutu, Jhosua Br Purba, Hany Mory Ferbiona Cristin Gultom Damanik, Yana Tasya Debora Sinaga, Debora Dhuha, Nadira Kaylana Eka Finanti Septiana Simamora Elsa Denada Elsa Noviyanti Sinaga Fadilla, Nia Febrianti, Dwi Ayu Fernando Purba Fitri Maulida Laila Gisty, Rival Ananda Gultom, Agnes Venita Harahap, Ade Novita Sari Hasibuan, Anisah Larasati Hutapea, Yonata Imel Simanungkalit Indri Agista Lubis, Nazwah Irwani, Dinda Izwita Dewi Laia, Lukman Hakim Lubis, Ariyanto Lubis, Nazlah Indri Agistia Lubis, Sutan Ismail Akbar Rafsanjani Maharani , Dwi Maigani, Maigani Manik, Ruth Sahanaya Manullang, Juliana Citra Manurung, Hendra Cahyadi Maria Munthe, Tiolina Marwa Khaerunnisa Masita, Nurul Mentari Sukma Meridina, Ramanda Nafa Cleo Wulandari Tarigan Naibaho, Joel Shintong Nainggolan, Gustia Louisa Naomi Tirta Bertua Serepina Tobing Nasution, Helina Qatrunnada Ndor Damayanti Silalahi Nova Marcelina Sitanggang Nurcahaya Br Zandroto Nurpadila, Nurpadila Panjaitan, Marojahan Purba, Diva Novita Angely Putri Purba, Elisa Jawari Putri Andini, Putri Putri Br Tarigan Putri, Imelda Rahmadani, Nisa Rahmah, Khalida Rizki, Putri Ryanti, Murni Nova Saing, Nasib Maruli Tua Samosir, Martha Indah Sianipar, Stevanus Binsar H Sibarani, Khoirunnisa Sidauruk, Vico Putra Sihotang, Harry Marcel Wahyu Silalahi, Lisbeth Grace Luciana Simangunsong, Erika Simanjuntak, Kasroni Simanjuntak, Rosi Ade Putri Sinaga, Sinta Marintan Sintia, Putri Mega Sinuhaji, Ribka Dameria Br Sinurat, Ade Putra Sinurat, Putra Paulus Sipayung, Ekklesia Sari Siregar, Anisa Rahmadani Siregar, Dea Athalia Siregar, Jhon Very Alihandro Siregar, Muhammad Alfi Sisilia Nababan Siti Sarah, Siti Sitindaon, David Micle Sitorus, Grace Elicia Situmeang, Jeki Chrisman Situmorang, Delia Situmorang, Immanuel Sulaiman, Raysah Puteri Syafitri, Nazwa Mutia Syahla, Elvy Anindya Tambunan, Engeli Emmanuela Tampubolon, Nora Vita Indahsari Tampubolon, Stephani Theresa Vania Tanjung, July Yanty Tarigan, Gita Helena Tarigan, Septi Agita Thresia Veronika Triani, Gihz Dhui Turnip, Leonardo Utami, Chintia Victory Rajani Sinaga Waniza, Elva Wardana, Aini Yarmita, Annisa Yolanda Marylandia Sitorus, Tabhita Zendrato, Mikhah Adillah